Trig Angle Formulas

What is the value of sin(π/12) using sum or difference identities?

• @@rac{ ext{√6}}{4} - rac{ ext{√2}}{4}@@

• @@rac{ ext{√3}}{2}@@

• @@rac{1}{2}@@

• @@rac{ ext{√2}}{2}@@

How do you express cos(175)cos(55) + sin(175)sin(55) using a double angle formula?

• Using the cosine of a difference formula: @@rac{{ ext{cos}(175) ext{cos}(55) + ext{sin}(175) ext{sin}(55)}}{{ ext{cos}(175 - 55)}} = ext{cos}(120)@@

• Using the sine of a sum formula: @@ ext{sin}(175 + 55) = ext{sin}(230)@@

• Using the sine of a difference formula: @@ ext{sin}(175 - 55) = ext{sin}(120)@@

• Using the cosine of a sum formula: @@ ext{cos}(175 + 55) = ext{cos}(230)@@

What is the value of sin(2u) when u = 45°?

• 0

• 0.5

• 1

• 0.707

How can you derive the double angle formula for cosine from the Pythagorean identity?

• @@rac{1}{2}( an^2(u) - 1)@@

• @@ an(2u) = rac{2 an(u)}{1 - an^2(u)}@@

• @@rac{1}{2}( an^2(u) + 1)@@

• @@ ext{cos}(2u) = ext{cos}^2(u) - ext{sin}^2(u) = 2 ext{cos}^2(u) - 1 = 1 - 2 ext{sin}^2(u)@@

What is the value of cos(2u) in terms of sin(u)?

• @@rac{1}{2} - rac{1}{2} ext{sin}^2(u)@@

• @@1 - 2 ext{sin}^2(u)@@

• @@ ext{sin}^2(u) - ext{cos}^2(u)@@

• @@ ext{cos}^2(u) - ext{sin}^2(u)@@

What is the double angle formula for cosine?

• \cos(2u) = \cos^2(u) - \sin^2(u)

• \cos(2u) = 2\sin^2(u) - 1

• \cos(2u) = 1 - 2\cos^2(u)

• \cos(2u) = \sin^2(u) + \cos^2(u)

What is the value of sin(2u) in terms of sin(u) and cos(u)?

• @@rac{{1}}{{2}} imes an(u)@@

• @@ an(2u) = rac{{2 an(u)}}{{1 - an^2(u)}}@@

• @@rac{{ an(u)}}{{ an(2u)}}@@

• @@ ext{sin}(2u) = 2 ext{sin}(u) ext{cos}(u)@@

What is the double angle formula for sine?

• \sin(2u) = 2\sin(u)\cos(u)

• \sin(2u) = \sin^2(u) - \cos^2(u)

• \sin(2u) = 2\sin^2(u)

• \sin(2u) = \cos(2u)

What is the value of sin(2u) when u = 30°?

• @@rac{ ext{1}}{ ext{2}}@@

• @@rac{ ext{ ext{√3}}}{ ext{2}}@@

• @@ ext{0}@@

• @@ ext{1}@@

What is the relationship between sin^2(u) and sin(2u)?

• @@rac{1 - ext{cos}(2u)}{2} = ext{sin}^2(u)@@

• @@ ext{sin}(2u) = 2 ext{sin}(u) ext{cos}(u)@@

• @@ ext{sin}^2(u) = ext{sin}(u) ext{cos}(u)@@

• @@ ext{sin}^2(u) = 1 - ext{cos}^2(u)@@